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java
7 months ago
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public class Solution {
    public static void main(String[] args) {
        // Example input
        int parentPos = 1;  // Initial position of parent
        int childPos = 10;  // Initial position of child
        int velParent = 3;  // Velocity of parent
        int steps = 10;     // Number of steps parent takes

        int[] result = calculateCommonFootstepsAndVelocity(parentPos, childPos, velParent, steps);
        System.out.println(result[0] + " " + result[1]); // Output: F and V2
    }

    private static int[] calculateCommonFootstepsAndVelocity(int parentPos, int childPos, int velParent, int steps) {
        int maxCommonSteps = 0;
        int bestVelocity = 0;

        // Assuming the velocity of the child can be at most twice the parent's
        for (int velChild = 1; velChild <= 2 * velParent; velChild++) {
            int commonSteps = 0;
            for (int step = 0; step < steps; step++) {
                int parentStepPos = parentPos + step * velParent;
                int childStepPos = childPos + step * velChild;
                
                if (parentStepPos == childStepPos) {
                    commonSteps++;
                }
            }

            if (commonSteps >= maxCommonSteps) {
                maxCommonSteps = commonSteps;
                bestVelocity = velChild;
            }
        }

        return new int[]{maxCommonSteps, bestVelocity};
    }
}
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